Internal problem ID [3732]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 478.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x -3 y\right ) y^{\prime }-y=-4-3 x} \]
✓ Solution by Maple
Time used: 0.875 (sec). Leaf size: 242
dsolve((x-3*y(x))*diff(y(x),x)+4+3*x-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{2}-\frac {\frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right )^{6} {\left (-144 \left (108 \left (2 x +3\right )^{3} c_{1} +12 \sqrt {-96 \left (2 x +3\right )^{9} c_{1}^{3}+81 \left (2 x +3\right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}-\frac {3456 \left (2 x +3\right )^{3} c_{1}}{\left (108 \left (2 x +3\right )^{3} c_{1} +12 \sqrt {-96 \left (2 x +3\right )^{9} c_{1}^{3}+81 \left (2 x +3\right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}+864 i \sqrt {3}\, \left (\frac {\left (108 \left (2 x +3\right )^{3} c_{1} +12 \sqrt {-96 \left (2 x +3\right )^{9} c_{1}^{3}+81 \left (2 x +3\right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}{6}-\frac {4 \left (2 x +3\right )^{3} c_{1}}{\left (108 \left (2 x +3\right )^{3} c_{1} +12 \sqrt {-96 \left (2 x +3\right )^{9} c_{1}^{3}+81 \left (2 x +3\right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}\right )\right )}^{2}}{2985984 c_{1}}-\left (2 x +3\right )^{3}}{2 \left (2 x +3\right )^{2}} \]
✓ Solution by Mathematica
Time used: 60.044 (sec). Leaf size: 793
DSolve[(x-3 y[x])y'[x]+4+3 x-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,1\right ]} y(x)\to \frac {x}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,2\right ]} y(x)\to \frac {x}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,3\right ]} y(x)\to \frac {x}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,4\right ]} y(x)\to \frac {x}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,5\right ]} y(x)\to \frac {x}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,6\right ]} \end{align*}