8.4.14 problem 14

Internal problem ID [717]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:59:05 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

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

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

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