Internal problem ID [3959]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number: Exact Differential equations. Exercise 9.17, page 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 23
dsolve([(y(x)^2*exp(x*y(x)^2)+4*x^3)+(2*x*y(x)*exp(x*y(x)^2)-3*y(x)^2)*diff(y(x),x)=0,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-{\mathrm e}^{\textit {\_Z}^{2} x}-x^{4}+\textit {\_Z}^{3}+2\right ) \]
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 23
DSolve[{(y[x]^2*Exp[x*y[x]^2]+4*x^3)+(2*x*y[x]*Exp[x*y[x]^2]-3*y[x]^2)*y'[x]==0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^4+e^{x y(x)^2}-y(x)^3=2,y(x)\right ] \]