Input:
pdsolve(ds(y,t)--y*ds(y,x)=v*ds(y,x,2)-ds(y,x,2)^2)
Write:
`pdsolve(ds(y,t)--y*ds(y,x)=v*ds(y,x,2)-ds(y,x,2)^2)`
Compute:
$$pdsolve(\frac{dy}{dt} +y\ \frac{dy}{dx} =v\ \frac{d^{{2}}y}{dx^{{2}}} - {(\frac{d^{{2}}y}{dx^{{2}}})}^{2})$$
Output:
$$pdsolve(\frac{dy}{dt} +y\ \frac{dy}{dx} =v\ \frac{d^{{2}}y}{dx^{{2}}} - {(\frac{d^{{2}}y}{dx^{{2}}})}^{2})== pdsolve(y^{(1)}(t)+y\ y^{(1)}(x)-v\ y^{(2)}(x)+{(y^{(2)}(x))}^{2},y)$$
Result: