Internal problem ID [77]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {3 y x +\left (x^{2}+4\right ) y^{\prime }-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 15
dsolve([3*x*y(x)+(x^2+4)*diff(y(x),x) = x,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{3}+\frac {16}{3 \left (x^{2}+4\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 22
DSolve[{3*x*y[x]+(x^2+4)*y'[x] == x,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {16}{3 \left (x^2+4\right )^{3/2}}+\frac {1}{3} \\ \end{align*}