Internal problem ID [548]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 6.
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: 0.156 (sec). Leaf size: 52
dsolve(diff(y(x),x) = (-a*x+b*y(x))/(b*x-c*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (c \,\textit {\_Z}^{2}-a -{\mathrm e}^{\RootOf \left (\left (\tanh ^{2}\left (\frac {\sqrt {a c}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 b}\right )\right ) a -a -{\mathrm e}^{\textit {\_Z}}\right )}\right ) x \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 58
DSolve[y'[x] == (-a*x+b*y[x])/(b*x-c*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {b \tanh ^{-1}\left (\frac {\sqrt {c} y(x)}{\sqrt {a} x}\right )}{\sqrt {a} \sqrt {c}}-\frac {1}{2} \log \left (\frac {c y(x)^2}{x^2}-a\right )=\log (x)+c_1,y(x)\right ] \]