40.3.10 problem 23 (p)

Internal problem ID [6614]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (p)
Date solved : Monday, January 27, 2025 at 02:15:55 PM
CAS classification : [_exact]

\begin{align*} 2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 41

dsolve((2*x*y(x)*exp(x^2*y(x))+ y(x)^2*exp(x*y(x)^2)+1)+(x^2*exp(x^2*y(x))+ 2*x*y(x)*exp(x*y(x)^2)-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} x^{4}+{\mathrm e}^{\frac {\textit {\_Z}^{2}}{x^{3}}} x^{4}+c_1 \,x^{4}+x^{5}-\textit {\_Z}^{2}\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.432 (sec). Leaf size: 30

DSolve[(2*x*y[x]*Exp[x^2*y[x]]+ y[x]^2*Exp[x*y[x]^2]+1)+(x^2*Exp[x^2*y[x]]+ 2*x*y[x]*Exp[x*y[x]^2]-2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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