60.1.203 problem 204

Internal problem ID [10217]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 204
Date solved : Monday, January 27, 2025 at 06:39:28 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y+a y+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.348 (sec). Leaf size: 56

dsolve(y(x)*diff(y(x),x)+a*y(x)+x=0,y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{\operatorname {RootOf}\left (\left (4 \,{\mathrm e}^{\textit {\_Z}} {\cosh \left (\frac {\sqrt {a^{2}-4}\, \left (2 c_{1} +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 a}\right )}^{2}+a^{2}-4\right ) x^{2}\right )}+1+a \textit {\_Z} \right ) x \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 38

DSolve[y[x]*D[y[x],x]+a*y[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]}{K[1]^2+a K[1]+1}dK[1]=-\log (x)+c_1,y(x)\right ] \]