Internal problem ID [1044]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {x^{2} {\mathrm e}^{x^{2}+y} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{x^{2}+y}-12 y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 27
dsolve((x^2*exp(x^2+y(x))*(2*x^2+3)+4*x)+(x^3*exp(x^2+y(x))-12*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ x^{3} {\mathrm e}^{y \relax (x )+x^{2}}-4 y \relax (x )^{3}+2 x^{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.44 (sec). Leaf size: 30
DSolve[(x^2*Exp[x^2+y[x]]*(2*x^2+3)+4*x)+(x^3*Exp[x^2+y[x]]-12*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 x^2+x^3 e^{x^2+y(x)}-4 y(x)^3=c_1,y(x)\right ] \]