44.6.53 problem 52 (c)

Internal problem ID [7197]
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 (c)
Date solved : Tuesday, February 04, 2025 at 12:47:12 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 (x_{0} \right )&=y_{0} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 34

dsolve([x*diff(y(x),x)-4*y(x)=x^6*exp(x),y(x__0) = y__0],y(x), singsol=all)
 

\[ y = \frac {x^{4} \left (\left (-x_{0}^{5}+x_{0}^{4}\right ) {\mathrm e}^{x_{0}}+x_{0}^{4} \left (x -1\right ) {\mathrm e}^{x}+y_{0} \right )}{x_{0}^{4}} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 35

DSolve[{x*D[y[x],x]-4*y[x]==x^6*Exp[x],{y[x0]==y0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4 \left (e^x (x-1) \text {x0}^4-e^{\text {x0}} (\text {x0}-1) \text {x0}^4+\text {y0}\right )}{\text {x0}^4} \]