Internal problem ID [3709]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 455.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (1+5 x -y\right ) y^{\prime }-5 y=-x -5} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 243
dsolve((1+5*x-y(x))*diff(y(x),x)+5+x-5*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {i \left (1-{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {2}{3}}+12 c_{1} x \right ) \sqrt {3}+6 \left (\left (2-{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}\right ) x +{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}\right ) c_{1} +{\left ({\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}-1\right )}^{2}}{6 c_{1} {\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 60.045 (sec). Leaf size: 925
DSolve[(1+5 x-y[x])y'[x]+5+x-5 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (186624 x^4+186624 e^{\frac {12 c_1}{25}} x^6\right )+\text {$\#$1}^5 \left (-186624 x^3-186624 e^{\frac {12 c_1}{25}} x^5\right )+\text {$\#$1}^4 \left (69984 x^2+77760 e^{\frac {12 c_1}{25}} x^4\right )+\text {$\#$1}^3 \left (-11664 x-17280 e^{\frac {12 c_1}{25}} x^3\right )+\text {$\#$1}^2 \left (729+2160 e^{\frac {12 c_1}{25}} x^2\right )-144 \text {$\#$1} e^{\frac {12 c_1}{25}} x+4 e^{\frac {12 c_1}{25}}\&,1\right ]}+5 x+1 \\ y(x)\to -\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (186624 x^4+186624 e^{\frac {12 c_1}{25}} x^6\right )+\text {$\#$1}^5 \left (-186624 x^3-186624 e^{\frac {12 c_1}{25}} x^5\right )+\text {$\#$1}^4 \left (69984 x^2+77760 e^{\frac {12 c_1}{25}} x^4\right )+\text {$\#$1}^3 \left (-11664 x-17280 e^{\frac {12 c_1}{25}} x^3\right )+\text {$\#$1}^2 \left (729+2160 e^{\frac {12 c_1}{25}} x^2\right )-144 \text {$\#$1} e^{\frac {12 c_1}{25}} x+4 e^{\frac {12 c_1}{25}}\&,2\right ]}+5 x+1 \\ y(x)\to -\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (186624 x^4+186624 e^{\frac {12 c_1}{25}} x^6\right )+\text {$\#$1}^5 \left (-186624 x^3-186624 e^{\frac {12 c_1}{25}} x^5\right )+\text {$\#$1}^4 \left (69984 x^2+77760 e^{\frac {12 c_1}{25}} x^4\right )+\text {$\#$1}^3 \left (-11664 x-17280 e^{\frac {12 c_1}{25}} x^3\right )+\text {$\#$1}^2 \left (729+2160 e^{\frac {12 c_1}{25}} x^2\right )-144 \text {$\#$1} e^{\frac {12 c_1}{25}} x+4 e^{\frac {12 c_1}{25}}\&,3\right ]}+5 x+1 \\ y(x)\to -\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (186624 x^4+186624 e^{\frac {12 c_1}{25}} x^6\right )+\text {$\#$1}^5 \left (-186624 x^3-186624 e^{\frac {12 c_1}{25}} x^5\right )+\text {$\#$1}^4 \left (69984 x^2+77760 e^{\frac {12 c_1}{25}} x^4\right )+\text {$\#$1}^3 \left (-11664 x-17280 e^{\frac {12 c_1}{25}} x^3\right )+\text {$\#$1}^2 \left (729+2160 e^{\frac {12 c_1}{25}} x^2\right )-144 \text {$\#$1} e^{\frac {12 c_1}{25}} x+4 e^{\frac {12 c_1}{25}}\&,4\right ]}+5 x+1 \\ y(x)\to -\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (186624 x^4+186624 e^{\frac {12 c_1}{25}} x^6\right )+\text {$\#$1}^5 \left (-186624 x^3-186624 e^{\frac {12 c_1}{25}} x^5\right )+\text {$\#$1}^4 \left (69984 x^2+77760 e^{\frac {12 c_1}{25}} x^4\right )+\text {$\#$1}^3 \left (-11664 x-17280 e^{\frac {12 c_1}{25}} x^3\right )+\text {$\#$1}^2 \left (729+2160 e^{\frac {12 c_1}{25}} x^2\right )-144 \text {$\#$1} e^{\frac {12 c_1}{25}} x+4 e^{\frac {12 c_1}{25}}\&,5\right ]}+5 x+1 \\ y(x)\to -\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (186624 x^4+186624 e^{\frac {12 c_1}{25}} x^6\right )+\text {$\#$1}^5 \left (-186624 x^3-186624 e^{\frac {12 c_1}{25}} x^5\right )+\text {$\#$1}^4 \left (69984 x^2+77760 e^{\frac {12 c_1}{25}} x^4\right )+\text {$\#$1}^3 \left (-11664 x-17280 e^{\frac {12 c_1}{25}} x^3\right )+\text {$\#$1}^2 \left (729+2160 e^{\frac {12 c_1}{25}} x^2\right )-144 \text {$\#$1} e^{\frac {12 c_1}{25}} x+4 e^{\frac {12 c_1}{25}}\&,6\right ]}+5 x+1 \\ \end{align*}