7.4.14 problem 14

Internal problem ID [86]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 14
Date solved : Friday, February 07, 2025 at 07:48:51 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-3 y&=x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

dsolve([x*diff(y(x),x)-3*y(x)=x^3,y(1) = 10],y(x), singsol=all)
 

\[ y = x^{3} \left (\ln \left (x \right )+10\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 13

DSolve[{x*D[y[x],x]-3*y[x]==x^3,{y[1]==10}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 (\log (x)+10) \]