Internal problem ID [11708]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-4 y-\left (x +5 y+3\right ) y^{\prime }=-10 x -12} \]
✓ Solution by Maple
Time used: 0.859 (sec). Leaf size: 129
dsolve((10*x-4*y(x)+12)-(x+5*y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-3 x -4\right ) {\operatorname {RootOf}\left (-1+\left (243 c_{1} x^{5}+1620 x^{4} c_{1} +4320 c_{1} x^{3}+5760 c_{1} x^{2}+3840 c_{1} x +1024 c_{1} \right ) \textit {\_Z}^{25}+\left (1458 c_{1} x^{5}+9720 x^{4} c_{1} +25920 c_{1} x^{3}+34560 c_{1} x^{2}+23040 c_{1} x +6144 c_{1} \right ) \textit {\_Z}^{20}+\left (2187 c_{1} x^{5}+14580 x^{4} c_{1} +38880 c_{1} x^{3}+51840 c_{1} x^{2}+34560 c_{1} x +9216 c_{1} \right ) \textit {\_Z}^{15}\right )}^{5}}{3}-2 x -3 \]
✓ Solution by Mathematica
Time used: 60.443 (sec). Leaf size: 3061
DSolve[(10*x-4*y[x]+12)-(x+5*y[x]+3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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