Internal problem ID [547]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 5.
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 {-a x -b y}{b x +c y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.148 (sec). Leaf size: 81
dsolve(diff(y(x),x) = (-a*x-b*y(x))/(b*x+c*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-b x c_{1}+\sqrt {-a c c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c}}{c c_{1}} \\ y \relax (x ) = -\frac {b x c_{1}+\sqrt {-a c c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c}}{c c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 135
DSolve[y'[x]== (-a*x-b*y[x])/(b*x+c*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {b x+\sqrt {x^2 \left (b^2-a c\right )+c e^{2 c_1}}}{c} \\ y(x)\to \frac {-b x+\sqrt {x^2 \left (b^2-a c\right )+c e^{2 c_1}}}{c} \\ y(x)\to -\frac {\sqrt {x^2 \left (b^2-a c\right )}+b x}{c} \\ y(x)\to \frac {\sqrt {x^2 \left (b^2-a c\right )}-b x}{c} \\ \end{align*}