32.3.13 problem Exact Differential equations. Exercise 9.17, page 79

Internal problem ID [5811]
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
Date solved : Monday, January 27, 2025 at 01:19:52 PM
CAS classification : [_exact]

\begin{align*} 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{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (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)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (-{\mathrm e}^{x \,\textit {\_Z}^{2}}-x^{4}+\textit {\_Z}^{3}+2\right ) \]

✓ Solution by Mathematica

Time used: 0.386 (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)*D[y[x],x]==0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
 

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