Internal problem ID [1933]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (x -3 y-5\right ) y^{\prime }=-3 x -1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 1.531 (sec). Leaf size: 84
dsolve([(3*x-y(x)+1)+(x-3*y(x)-5)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y = \frac {\left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {4}{3}}-12 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}} x -84 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}}+576 x^{2}+1152 x +576}{36 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 60.756 (sec). Leaf size: 341
DSolve[{(3*x-y[x]+1)+(x-3*y[x]-5)*y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-5 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]} \]