64.5.21 problem 21

Internal problem ID [13334]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 05:22:41 AM
CAS classification : [_linear]

\begin{align*} {\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 14

dsolve([exp(x)*(y(x)-3*(exp(x)+1)^2)+(exp(x)+1)*diff(y(x),x)=0,y(0) = 4],y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}+1 \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 12

DSolve[{Exp[x]*(y[x]-3*(Exp[x]+1)^2)+(Exp[x]+1)*D[y[x],x]==0,{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (e^x+1\right )^2 \]