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`]]
\[ \boxed {\left (x -3 y\right ) y^{\prime }-y=-3 x -4} \]
✓ Solution by Maple
Time used: 1.875 (sec). Leaf size: 227
dsolve((x-3*y(x))*diff(y(x),x)+4+3*x-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {i \left (-36864 \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}+\left (864 c_{1} x^{3}+3888 c_{1} x^{2}+5832 c_{1} x +12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+2916 c_{1} \right )^{\frac {4}{3}}\right ) \sqrt {3}+36864 \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}-48 \left (12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+864 \left (x +\frac {3}{2}\right )^{3} c_{1} \right )^{\frac {2}{3}} \left (x +3\right ) \left (3+2 x \right )^{2} c_{1} +\left (864 c_{1} x^{3}+3888 c_{1} x^{2}+5832 c_{1} x +12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+2916 c_{1} \right )^{\frac {4}{3}}}{144 \left (12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+864 \left (x +\frac {3}{2}\right )^{3} c_{1} \right )^{\frac {2}{3}} c_{1} \left (3+2 x \right )^{2}} \]
✓ 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*}