60.1.390 problem 391

Internal problem ID [10404]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 391
Date solved : Monday, January 27, 2025 at 07:40:01 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

\begin{align*} y &= c_{1} {\mathrm e}^{-a x} \\ y &= -\frac {b \,x^{2}}{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 34

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

\begin{align*} y(x)\to c_1 e^{-a x} \\ y(x)\to -\frac {b x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}