15.5.18 problem 22

Internal problem ID [2954]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 22
Date solved : Monday, January 27, 2025 at 07:00:28 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (2\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.117 (sec). Leaf size: 22

dsolve([(x^2*y(x)^2-y(x))+(2*x^3*y(x)+x)*diff(y(x),x)=0,y(2) = -2],y(x), singsol=all)
 

\[ y = \frac {-1-\sqrt {28 x^{3}+1}}{2 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.877 (sec). Leaf size: 34

DSolve[{(x^2*y[x]^2-y[x])+(2*x^3*y[x]+x)*D[y[x],x]==0,{y[2]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt {\frac {1}{x^2}} \sqrt {28 x^3+1} x+1}{2 x^2} \]