# Toronto Math Forum

## APM346-2015F => APM346--Home Assignments => HA1 => Topic started by: Emily Deibert on September 29, 2015, 08:40:23 PM

Title: Problem 5
Post by: Emily Deibert on September 29, 2015, 08:40:23 PM
5.
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter1/S1.P.html#problem-1.P.5 (http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter1/S1.P.html#problem-1.P.5)
a)
u = y\int\Bigg(\int f(x)dx\Bigg)dx + \int\Bigg(\int g(x)dx\Bigg)dx + xh(y) + j(y)

b)
u = \int \int f(x,y)dydz + \int g(x,z)dx + h(y,z)

c)
u = sin(x)sin(y) + y\int \Bigg(\int f(x)dx \Bigg)dx + \int \Bigg(\int g(x)dx\Bigg)dx + xh(y) + j(y)

d)
u = -cos(x)cos(y)cos(z) + \int \int f(x,y)dydx + \int g(x,z)dx + h(y,z)

e)
u = -yzcos(x) - xzcos(y) - xycos(z) + \int \int f(x,y)dydx + \int g(x,z)dx + h(y,z)
Title: Re: Problem 5
Post by: Andrew Lee Chung on September 30, 2015, 04:21:26 PM
My take on problem 5:
For b) shouldn't it be:

u = \int \int f(x,y)dydx + \int g(x,z)dx + h(y,z)

Also is it safe to assume $$\int \int f(x,y)dydx = f_{2}(x,y)$$
for convenience?

So that we can rewrite it as:
$$u = f_{2}(x,y) + g_{1}(x,z) + h(y,z)$$

The rest seems fine
Title: Re: Problem 5
Post by: Victor Ivrii on October 03, 2015, 05:41:05 AM
Good, but please use the simplest notations so
\begin{gather}
u= f(x)+f_1(x)y+g(y)+g_1(y)x,\\
u=f(x,y)+g(x,z)+h(y,z),\\
u=\sin(x)\sin(y)+ f(x)+f_1(x)y+g(y)+g_1(y)x,\\
u=-\cos(x)\cos(y)\cos(z)+f(x,y)+g(x,z)+h(y,z),\\
u=-yz\cos(x)-xz\cos(y)-xy\cos(z)+f(x,y)+g(x,z)+h(y,z)
\end{gather}