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enter image description here

how we write this equation in latex in given form

  • 9
    Nice try, but even the most comprehensive answer won't help you much. You won't get written all of your equations here. Learn LaTeX. Read an introduction and the command texdoc packagenameis a great help. – Keks Dose Feb 14 at 11:58
  • 2
    Welcome to Stack Exchange! It looks like there's already a few solutions posted below. Great. However may I suggest that next time you ask a question, mention what you have already tried. e.g. Have you figured out how to write a gamma on its own? Have you figured out how to write a fraction? How to write du/dz? etc. The more effort you demonstrate you have put in, the more effort others will be willing to put in for you. It also helps us understand precisely which part of the task you need help with. – falsePockets Feb 15 at 4:49
  • I have downvoted, because this question does not show any research effort. – gerrit Feb 15 at 8:08
24

With a few shortcut macros it's much easier:

plain TeX version:

\let~\catcode~`86~`j0~`X13~`C1~`D2~`M3jdefX81C~`8113jdefDXZZ81C~
`8113DXYY81CZ81jletDYLLjletYFFjfiYNNjdefYPPjpartialZIZAZBZj{Zj}Y
EEjexpandafterYOOjelseYKKjifxNI818283CL}81NAC82DNBC83Djfuturelet
jTjHDNjHCKjT}L{AOL{BF{DXUUCI)jpCjp)CDDDY VVjoverNjp)818283CKX81X
CP82VP83DOCP^C81D82VjbC81DC83DDFDYRRjrelaxNjb8182Cjd8182RDNjd81%
8283CK83RP82^C81DOP82P83FDY!!uY@@vY##wY$$xYj%%yY&&zXvv81C81^2DMM
!U!$+@U!%+#U!&+jlambda_1jleft(v!U)2! $+v@U)2!%+v#U)2!&jatop+2!@U
)2!C$%D+2@#U)2!C%&D+2!#U)2!C$&Djright)=jnuU)2!&jeqno(1.25)MMjbye

LaTeX version:

\documentclass{article}\begin{document}
\let~\catcode~`86~`j0~`X13~`C1~`D2~`M3jdefX81C~`8113jdefDXZZ81C~
`8113DXYY81CZ81jletDYLLjletYFFjfiYNNjdefYPPjpartialZIZAZBZj{Zj}Y
EEjexpandafterYOOjelseYKKjifxNI818283CL}81NAC82DNBC83Djfuturelet
jTjHDNjHCKjT}L{AOL{BF{DXUUCI)jpCjp)CDDDY VVjoverNjp)818283CKX81X
CP82VP83DOCP^C81D82VjbC81DC83DDFDYRRjrelaxNjb8182Cjd8182RDNjd81%
8283CK83RP82^C81DOP82P83FDY!!uY@@vY##wY$$xYj%%yY&&zXvv81C81^2DMM
!U!$+@U!%+#U!&+jlambda_1jleft(v!U)2!$+v@U)2!%+v#U)2!&jatop+2!@U)
2!C$%D+2@#U)2!C%&D+2!#U)2!C$&Djright)=jnuU)2!&jeqno(1.25)MMjstop

output:

enter image description here


Inspired by David Carlisle's xii :)

  • 7
    +1 for snarkiness. – Jacob Manaker Feb 14 at 22:32
  • I don't think MiKTeX gave me a TeX engine. – ahorn May 20 at 21:09
  • @ahorn Sorry, I don't understand what you mean. You didn't find the tex executable? – Phelype Oleinik May 20 at 21:11
  • @PhelypeOleinik I just don't know how to run TeX code, so I thought I'd leave a comment. Sorry for the clutter. – ahorn May 20 at 21:52
  • @ahorn No worries, we can delete them later :-) Do you run LaTeX from the command line or from an IDE? If the latter, then which one? TeXMaker? TeXStudio? Another? – Phelype Oleinik May 20 at 23:59
5

Here you go:

\documentclass[10pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\begin{document}
    $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}+\lambda_1\begin{pmatrix}
    u^2\frac{\partial^2 u}{\partial x^2}+v\frac{\partial^2 u}{\partial y^2}+w^2\frac{\partial^2 u}{\partial z^2}\\+2uv\frac{\partial^2 u}{\partial x\partial y}+2vw\frac{\partial^2 u}{\partial y\partial z}+2uw\frac{\partial^2 u}{\partial x\partial z}
    \end{pmatrix} = v\frac{\partial^2 u}{\partial z^2},$
\end{document}

this will give you:

enter image description here

PS: Welcome to TeX.se, from next time, please provide a MWE.

5

A variation on the theme, but with a greater emphasis on simplifying the input:

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}

\newcommand{\pdiff}{\mathop{}\!\partial}

\ExplSyntaxOn
\NewDocumentCommand{\pder}{omm}
 {
  \frac{\pdiff\IfValueT{#1}{^{#1}}#2}{\faisal_pder_vars:n { #3 }}
 }
\cs_new_protected:Nn \faisal_pder_vars:n
 {
  \clist_map_inline:nn { #1 } { \pdiff##1 }
 }
\ExplSyntaxOff


\begin{document}

\begin{equation}
u\pder{u}{x}+v\pder{u}{y}+w\pder{u}{z}+
  \lambda_1
  \left(\begin{gathered}
    u^2\pder[2]{u}{x^2}+v\pder[2]{u}{y^2}+w^2\pder[2]{u}{z^2}\\
    \mspace{-\medmuskip}{}
    +2uv\pder[2]{u}{x,y}+2vw\pder[2]{u}{y,z}+2uw\pder[2]{u}{x,z}
    \end{gathered}\right)
= \nu\pder[2]{u}{z^2},
\end{equation}

\begin{equation}
\begin{split}
u\pder{u}{x}&+v\pder{u}{y}+w\pder{u}{z}
+\lambda_1\biggl(
    u^2\pder[2]{u}{x^2}+v\pder[2]{u}{y^2}+w^2\pder[2]{u}{z^2}
\\
&+2uv\pder[2]{u}{x,y}+2vw\pder[2]{u}{y,z}+2uw\pder[2]{u}{x,z}\biggr)
= \nu\pder[2]{u}{z^2},
\end{split}
\end{equation}

\end{document}

The syntax for \pder is

  1. optional argument for the order of the derivative (if greater than 1)
  2. function to differentiate
  3. list of the variables the derivative is taken with respect to, comma separated

In the first case I used \mspace{-\medmuskip}{}+ in order to have the plus sign correctly spaced. I used gathered instead of pmatrix because it is semantically sounder.

enter image description here

3

Here is a start:

\documentclass[]{article}
\usepackage{amsmath}

\begin{document}
\begin{equation}
    u\frac{\partial u}{\partial x}+...
    +\lambda_1 
    \begin{pmatrix}
    u^2 \frac{\partial^2 u}{\partial x^2}+...\\
    + 2 uv \frac{\partial^2 u}{\partial x \partial y}+...
    \end{pmatrix} = v \frac{\partial^2 u}{\partial z^2}
\end{equation}
\end{document}

enter image description here

  • 3
    Please, edit your code and replace ... by \dots (or \cdots when not between two plus signs). – Sigur Feb 14 at 13:20
  • 4
    @Sigur I have added the three dots to indicate to OP that he has to complete the equation by himself. The final version of the equation should not have dots within it. – Hafid Boukhoulda Feb 14 at 16:59
2

Borrow a little from all answer and make a little change (such as change v to \nu in the right-hand side)

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
    u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}+\lambda_1\begin{pmatrix}
    u^2\frac{\partial^2 u}{\partial x^2}+v\frac{\partial^2 u}{\partial y^2}+w^2\frac{\partial^2 u}{\partial z^2}\\+2uv\frac{\partial^2 u}{\partial x\partial y}+2vw\frac{\partial^2 u}{\partial y\partial z}+2uw\frac{\partial^2 u}{\partial x\partial z}
    \end{pmatrix} = \nu\frac{\partial^2 u}{\partial z^2},
    \tag{1.25}
\end{equation}
\end{document}

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