Internal problem ID [8564]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 228.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (4 y+11 x -11\right ) y^{\prime }-25 y=8 x -62} \]
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 377
dsolve((4*y(x)+11*x-11) *diff(y(x),x)-25*y(x)-8*x+62=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {22}{9}+\frac {36 \left (9 x -1\right ) \left (-\frac {\left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}{27}-\frac {16}{27 \left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}-\frac {19}{27}+2 i \sqrt {3}\, \left (\frac {\left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}{54}-\frac {8}{27 \left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )\right )}{-3 \left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}-\frac {48}{\left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}+24+162 i \sqrt {3}\, \left (\frac {\left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}{54}-\frac {8}{27 \left (64-8748 \left (9 x -1\right )^{2} c_{1} +108 \sqrt {6561 \left (9 x -1\right )^{4} c_{1}^{2}-96 \left (9 x -1\right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )} \]
✓ Solution by Mathematica
Time used: 60.17 (sec). Leaf size: 1677
DSolve[(4*y[x]+11*x-11)*y'[x]-25*y[x]-8*x+62==0,y[x],x,IncludeSingularSolutions -> True]
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