83.22.11 problem 11

Internal problem ID [19265]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 01:17:48 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y-x y^{\prime }&=x +y^{\prime } y \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 24

dsolve(y(x)-x*diff(y(x),x)=x+y(x)*diff(y(x),x),y(x), singsol=all)
 

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 34

DSolve[y[x]-x*D[y[x],x]==x+y[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\arctan \left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]