29.15.23 problem 431

Internal problem ID [5029]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 431
Date solved : Tuesday, January 28, 2025 at 02:41:22 PM
CAS classification : [NONE]

\begin{align*} y^{\prime } y+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 30

dsolve(y(x)*diff(y(x),x)+x+f(x^2+y(x)^2)*g(x) = 0,y(x), singsol=all)
 

\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}}{f \left (\textit {\_a}^{2}+x^{2}\right )}d \textit {\_a} +\int g \left (x \right )d x -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.298 (sec). Leaf size: 95

DSolve[y[x] D[y[x],x]+x+f[x^2+y[x]^2] g[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{f\left (x^2+K[2]^2\right )}-\int _1^x-\frac {2 K[1] K[2] f''\left (K[1]^2+K[2]^2\right )}{f\left (K[1]^2+K[2]^2\right )^2}dK[1]\right )dK[2]+\int _1^x\left (g(K[1])+\frac {K[1]}{f\left (K[1]^2+y(x)^2\right )}\right )dK[1]=c_1,y(x)\right ] \]