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`]]
\[ \boxed {y^{\prime }-\frac {-a x +y b}{b x -c y}=0} \]
✓ Solution by Maple
Time used: 0.609 (sec). Leaf size: 52
dsolve(diff(y(x),x) = (-a*x+b*y(x))/(b*x-c*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (c \,\textit {\_Z}^{2}-a -{\mathrm e}^{\operatorname {RootOf}\left (\tanh \left (\frac {\sqrt {a c}\, \left (2 c_{1} +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 b}\right )^{2} a -a -{\mathrm e}^{\textit {\_Z}}\right )}\right ) x \]
✓ 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]
\[ \text {Solve}\left [-\frac {b \text {arctanh}\left (\frac {\sqrt {c} y(x)}{\sqrt {a} x}\right )}{\sqrt {a} \sqrt {c}}-\frac {1}{2} \log \left (\frac {c y(x)^2}{x^2}-a\right )=\log (x)+c_1,y(x)\right ] \]