Internal problem ID [3224]
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]]
Solve \begin {gather*} \boxed {\left (-3 y+x \right ) y^{\prime }+4+3 x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.139 (sec). Leaf size: 242
dsolve((x-3*y(x))*diff(y(x),x)+4+3*x-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{2}-\frac {\frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right )^{6} \left (-144 \left (108 \left (3+2 x \right )^{3} c_{1}+12 \sqrt {-96 \left (3+2 x \right )^{9} c_{1}^{3}+81 \left (3+2 x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}-\frac {3456 \left (3+2 x \right )^{3} c_{1}}{\left (108 \left (3+2 x \right )^{3} c_{1}+12 \sqrt {-96 \left (3+2 x \right )^{9} c_{1}^{3}+81 \left (3+2 x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}+864 i \sqrt {3}\, \left (\frac {\left (108 \left (3+2 x \right )^{3} c_{1}+12 \sqrt {-96 \left (3+2 x \right )^{9} c_{1}^{3}+81 \left (3+2 x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}{6}-\frac {4 \left (3+2 x \right )^{3} c_{1}}{\left (108 \left (3+2 x \right )^{3} c_{1}+12 \sqrt {-96 \left (3+2 x \right )^{9} c_{1}^{3}+81 \left (3+2 x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}\right )\right )^{2}}{2985984 c_{1}}-\left (3+2 x \right )^{3}}{2 \left (3+2 x \right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 781
DSolve[(x-3 y[x])y'[x]+4+3 x-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (x-\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,1\right ]}\right ) \\ y(x)\to \frac {1}{3} \left (x-\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,2\right ]}\right ) \\ y(x)\to \frac {1}{3} \left (x-\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,3\right ]}\right ) \\ y(x)\to \frac {1}{3} \left (x-\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,4\right ]}\right ) \\ y(x)\to \frac {1}{3} \left (x-\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,5\right ]}\right ) \\ y(x)\to \frac {1}{3} \left (x-\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+9216 x^5+34560 x^4+69120 x^3+77760 x^2+46656 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-384 x^4-2304 x^3-5184 x^2-5184 x-1944\right )+\text {$\#$1}^3 \left (64 x^3+288 x^2+432 x+216\right )+\text {$\#$1}^2 \left (36 x^2+108 x+81\right )+\text {$\#$1} (-12 x-18)+1\&,6\right ]}\right ) \\ \end{align*}