Internal problem ID [6280]
Book: Selected problems from homeworks from different courses
Section: Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college,
Bloomington, Minnesota
Problem number: HW 1 problem 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-y+2 x}{x +4 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.36 (sec). Leaf size: 19
dsolve([diff(y(x),x)=(2*x-y(x))/(x+4*y(x)),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{4}+\frac {\sqrt {9 x^{2}+16}}{4} \]
✓ Solution by Mathematica
Time used: 0.744 (sec). Leaf size: 24
DSolve[{y'[x]==(2*x-y[x])/(x+4*y[x]),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\sqrt {9 x^2+16}-x\right ) \\ \end{align*}