# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

45 views

### Solving this ODE 1

Trouble solving this ODE : $$\frac{d^2y}{dx^2}=\int_{-\infty}^{x^2/2} e^{x-t^2/2} \, \mathrm{d}t$$ $$x>0,\, y(0)=0,\, \frac{dy}{dx}(0)=0$$ in the form $$y(x)=\int_{0}^{x} h(t) \, \mathrm{d}t$$ ...
28 views

20 views

### finding solution to $u_x + 2u_y + (2x − y)u = 2x^2 + 3xy − 2y^2$

I tried to solve this equation with the coordinate method but I got a bit different answer compared to the suggested one by the solution manual. Where I am making the mistake in my solution? My ...
23 views

### finding solution to $au_x+bu_y=f(x,y)$ where $a \neq 0$

I can't get the solution in the required form of $$u(x,y)=(a^2+b^2)^{-\frac{1}{2}}\int_{L}fds +g(bx-ay)$$ "where g is an arbitrary function of one variable, L is the characteristic line segment from ...
37 views

### Show that if $T(x)=\int_0^\infty e^{-t}t^{x-1}dt$, then $T(1)=1$

I need to calculate the following Given: $T(x)=\int_0^\infty e^{-t}t^{x-1}dt$ I need to show that $T(1)=1$ Solution: My logic was to plug $1$ in for $x$ before I integrated, but I am not ...
29 views

21 views

### Existence and uniqueness of an ODE solution across simple discontinuities

I am studying differential equations using MIT's publicly available materials. One of the exercises runs as follows: Let $I = (a,b)$ be an open interval containing $0$, and consider the ODE \begin{...
26 views

### Solving ODE by substitution. Where does $dy$ goes
When solving ODE by substitution, where does $dy$ goes from the following example? $$\left(1+\frac{sin(y)}{cos(y)}\right)dy=x dx$$ Let $u=-cos(y)$. Hence $du = sin(y)$, which results in the following: ...
Just as a bit of background, I'm working with the Black-Scholes PDE and I'm testing some things out by taking an initial condition for it as $\sin(S/50)$, where $S$ is the spot price (but that's ...