8.4.24 problem 24

Internal problem ID [727]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:59:19 AM
CAS classification : [_separable]

\begin{align*} 3 y x +\left (x^{2}+4\right ) y^{\prime }&=x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 15

dsolve([3*x*y(x)+(x^2+4)*diff(y(x),x) = x,y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {1}{3}+\frac {16}{3 \left (x^{2}+4\right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 22

DSolve[{3*x*y[x]+(x^2+4)*D[y[x],x] == x,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {16}{3 \left (x^2+4\right )^{3/2}}+\frac {1}{3} \]