23.1.27 problem 2(q)

Internal problem ID [4117]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(q)
Date solved : Monday, January 27, 2025 at 08:36:38 AM
CAS classification : [_exact, _rational]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.095 (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)
 

\[ y \left (x \right ) = \frac {\left (12+4 x^{3}+4 \sqrt {x^{6}+10 x^{3}+9}\right )^{{2}/{3}}-4 x}{2 \left (12+4 x^{3}+4 \sqrt {x^{6}+10 x^{3}+9}\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 3.974 (sec). Leaf size: 66

DSolve[{(x+y[x]^2)*D[y[x],x]+(y[x]-x^2)==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt [3]{x^3+\sqrt {x^6+10 x^3+9}+3}}{\sqrt [3]{2}}-\frac {\sqrt [3]{2} x}{\sqrt [3]{x^3+\sqrt {x^6+10 x^3+9}+3}} \]