15.5.15 problem 15

Internal problem ID [2951]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:00:20 AM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} 2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 28

dsolve(2*x^2*y(x)*diff(y(x),x)+(x^4*exp(x)-2*x*y(x)^2)=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-{\mathrm e}^{x}+c_1}\, x \\ y &= -\sqrt {-{\mathrm e}^{x}+c_1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.459 (sec). Leaf size: 45

DSolve[2*x^2*y[x]*D[y[x],x]+(x^4*Exp[x]-2*x*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

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