Internal problem ID [2519]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(q).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {\left (x +y^{2}\right ) y^{\prime }+y-x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 56
dsolve([(x+y(x)^2)*diff(y(x),x)+(y(x)-x^2)=0,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (12+4 x^{3}+4 \sqrt {x^{6}+10 x^{3}+9}\right )^{\frac {2}{3}}-4 x}{2 \left (12+4 x^{3}+4 \sqrt {x^{6}+10 x^{3}+9}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 3.853 (sec). Leaf size: 66
DSolve[{(x+y[x]^2)*y'[x]+(y[x]-x^2)==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x^3+\sqrt {x^6+10 x^3+9}+3}}{\sqrt [3]{2}}-\frac {\sqrt [3]{2} x}{\sqrt [3]{x^3+\sqrt {x^6+10 x^3+9}+3}} \\ \end{align*}