60.1.35 problem 35

Internal problem ID [10049]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 35
Date solved : Monday, January 27, 2025 at 06:19:38 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 35

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

\[ y = -a +\tanh \left (\sqrt {a^{2}-b}\, \left (\int fd x +c_{1} \right )\right ) \sqrt {a^{2}-b} \]

✓ Solution by Mathematica

Time used: 0.320 (sec). Leaf size: 83

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+2 a K[1]+b}dK[1]\&\right ]\left [\int _1^x-f(K[2])dK[2]+c_1\right ] \\ y(x)\to -\sqrt {a^2-b}-a \\ y(x)\to \sqrt {a^2-b}-a \\ \end{align*}