60.1.216 problem 217

Internal problem ID [10230]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 217
Date solved : Monday, January 27, 2025 at 06:40:28 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

dsolve((y(x)-x^2)*diff(y(x),x)-x=0,y(x), singsol=all)
 

\[ y = x^{2}+\frac {\operatorname {LambertW}\left (-4 c_{1} {\mathrm e}^{-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 4.052 (sec). Leaf size: 40

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

\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{-2 x^2-1+c_1}\right )\right ) \\ y(x)\to x^2+\frac {1}{2} \\ \end{align*}