2.28 ODE No. 28
- Problem in Latex
- Mathematica input
- Maple input
✓ Mathematica : cpu = 0.102271 (sec), leaf count = 96
✓ Maple : cpu = 0.073 (sec), leaf count = 51
This is Riccati first order non-linear ODE with . We can convert Riccati to Bernoulli which
is easier to solve using the substitution or
This is of the form and since then it is Bernoulli differential equation. (when and it is
Riccati). To solve Bernoulli we always start by dividing by Then we let , hence , therefore
the above becomes
Integrating factor is , hence Integrating both sides gives , hence from above
Since then
And since then
Verification
eq:=diff(y(x),x)+x*y(x)^2-x^3*y(x)-2*x = 0;
sol:=x^2+ exp(-x^4/4)/(_C1+ sqrt(Pi)/2*erf(x^2/2));
odetest(y(x)=sol,eq);
0