73.1.23 problem 2.4 (a)

Internal problem ID [15001]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.4 (a)
Date solved : Tuesday, January 28, 2025 at 07:27:19 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=40 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 16

dsolve([diff(y(x),x)=4*x*10*exp(2*x),y(0) = 4],y(x), singsol=all)
 

\[ y = 14+\left (20 x -10\right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 24

DSolve[{D[y[x],x]==4*x*10*Exp[2*x],{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _0^x40 e^{2 K[1]} K[1]dK[1]+4 \]