60.1.200 problem 201

Internal problem ID [10214]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 201
Date solved : Monday, January 27, 2025 at 06:39:24 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 21

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

\[ y = i \tan \left (-i \left (\int \sqrt {f}d x \right )+c_{1} \right ) \sqrt {f} \]

✓ Solution by Mathematica

Time used: 0.259 (sec). Leaf size: 39

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

\[ y(x)\to i \sqrt {f(x)} \tan \left (i \int _1^x-\sqrt {f(K[1])}dK[1]+c_1\right ) \]