Internal problem ID [5271]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {2 x y \,{\mathrm e}^{y x^{2}}+y^{2} {\mathrm e}^{x y^{2}}+\left (x^{2} {\mathrm e}^{y x^{2}}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.385 (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])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{x^2 y(x)}-y(x)^2+e^{x y(x)^2}+x=c_1,y(x)\right ] \]