60.1.34 problem 34

Internal problem ID [10048]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 34
Date solved : Monday, January 27, 2025 at 06:19:36 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

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

\[ y = \frac {{\mathrm e}^{-\int g \left (x \right )d x}}{\int {\mathrm e}^{-\int g \left (x \right )d x} fd x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 59

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

\begin{align*} y(x)\to \frac {\exp \left (\int _1^x-g(K[1])dK[1]\right )}{-\int _1^x-\exp \left (\int _1^{K[2]}-g(K[1])dK[1]\right ) f(K[2])dK[2]+c_1} \\ y(x)\to 0 \\ \end{align*}