73.7.37 problem 37

Internal problem ID [15195]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 37
Date solved : Tuesday, January 28, 2025 at 07:41:37 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime } y-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 43

dsolve(y(x)*diff(y(x),x)-x*y(x)^2=6*x*exp(4*x^2),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {{\mathrm e}^{x^{2}} \left (2 \,{\mathrm e}^{3 x^{2}}+c_{1} \right )} \\ y &= -\sqrt {{\mathrm e}^{x^{2}} \left (2 \,{\mathrm e}^{3 x^{2}}+c_{1} \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.991 (sec). Leaf size: 62

DSolve[y[x]*D[y[x],x]-x*y[x]^2==6*x*Exp[4*x^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -e^{\frac {x^2}{2}} \sqrt {2 e^{3 x^2}+c_1} \\ y(x)\to e^{\frac {x^2}{2}} \sqrt {2 e^{3 x^2}+c_1} \\ \end{align*}