Internal problem ID [4025]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.12, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {y^{2} {\mathrm e}^{y^{2} x}+4 x^{3}+\left (2 x y \,{\mathrm e}^{y^{2} x}-3 y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 21
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(x), singsol=all)
\[ {\mathrm e}^{x y \relax (x )^{2}}+x^{4}-y \relax (x )^{3}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 24
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[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^4+e^{x y(x)^2}-y(x)^3=c_1,y(x)\right ] \]