44.6.51 problem 52 (a)

Internal problem ID [7195]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 52 (a)
Date solved : Tuesday, February 04, 2025 at 12:46:45 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

dsolve([x*diff(y(x),x)-4*y(x)=x^6*exp(x),y(0) = 0],y(x), singsol=all)
 

\[ y = x^{4} \left ({\mathrm e}^{x} \left (x -1\right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.096 (sec). Leaf size: 19

DSolve[{x*D[y[x],x]-4*y[x]==x^6*Exp[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^4 \left (e^x (x-1)+c_1\right ) \]