60.1.28 problem 28

Internal problem ID [10042]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 28
Date solved : Monday, January 27, 2025 at 06:19:18 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 74

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

\begin{align*} y(x)\to \frac {e \sqrt {\pi } x^2 \text {erf}\left (\frac {x^2}{2}\right )+2 e^{1-\frac {x^4}{4}}+2 c_1 x^2}{e \sqrt {\pi } \text {erf}\left (\frac {x^2}{2}\right )+2 c_1} \\ y(x)\to x^2 \\ \end{align*}