60.1.44 problem 44

Internal problem ID [10058]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 44
Date solved : Monday, January 27, 2025 at 06:20:02 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+2 a \,x^{3} y^{3}+2 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 53

dsolve(diff(y(x),x) + 2*a*x^3*y(x)^3 + 2*x*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {2}{\sqrt {-4 a \,x^{2}+4 c_{1} {\mathrm e}^{2 x^{2}}-2 a}} \\ y &= \frac {2}{\sqrt {-4 a \,x^{2}+4 c_{1} {\mathrm e}^{2 x^{2}}-2 a}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.488 (sec). Leaf size: 70

DSolve[D[y[x],x] + 2*a*x^3*y[x]^3 + 2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {-\frac {1}{2} a \left (2 x^2+1\right )+c_1 e^{2 x^2}}} \\ y(x)\to \frac {1}{\sqrt {-\frac {1}{2} a \left (2 x^2+1\right )+c_1 e^{2 x^2}}} \\ y(x)\to 0 \\ \end{align*}