60.1.274 problem 275

Internal problem ID [10288]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 275
Date solved : Monday, January 27, 2025 at 06:50:29 PM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 36

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

\[ \frac {{\mathrm e}^{-2 i y} \left (i x +y\right )+2 c_{1} \left (x +i y\right )}{2 i y+2 x} = 0 \]

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 91

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

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