15.3.11 problem 11
Internal
problem
ID
[2904]
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
Date
solved
:
Monday, January 27, 2025 at 06:28:14 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 3 x -y+1+\left (x -3 y-5\right ) y^{\prime }&=0 \end{align*}
With initial conditions
\begin{align*} y \left (0\right )&=0 \end{align*}
✓ Solution by Maple
Time used: 4.405 (sec). Leaf size: 113
dsolve([(3*x-y(x)+1)+(x-3*y(x)-5)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[
y = \frac {\left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{4}/{3}}-12 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{2}/{3}} x -84 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{2}/{3}}+576 x^{2}+1152 x +576}{36 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{2}/{3}}}
\]
✓ Solution by Mathematica
Time used: 60.813 (sec). Leaf size: 341
DSolve[{(3*x-y[x]+1)+(x-3*y[x]-5)*D[y[x],x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to \frac {x \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-5 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]}
\]