12.6.15 problem 15

Internal problem ID [1694]
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
Date solved : Monday, January 27, 2025 at 05:29:35 AM
CAS classification : [_exact]

\begin{align*} x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ x^{3} {\mathrm e}^{y+x^{2}}-4 y^{3}+2 x^{2}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.484 (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)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 x^2+x^3 e^{x^2+y(x)}-4 y(x)^3=c_1,y(x)\right ] \]