Differential Equations Answers

Find the integral surface of 𝑥²𝑝 + 𝑦²𝑞 + 𝑧² = 0 which passes through the curve x+y = xy, 𝑧= 1.

Solve the following initial value problem

Ut(x,t)=10Uxx(x,t) -10

U(-1,t)=U(1,t) Ux(-1,t)=Ux(1,t) t>0

Ux(x,0)=x+1 -1

Solve the differential equation by separation of variables with step-by-step procedures.

(x+2)dx = (x+3) siny cosydy

Solve the differential equation by separation of variables.

(x^3 + 2)y = x(y^4 + 3)y’ ; at x = 1 and y = 1

Suppose you discover an expired library book in the attic for which your great-great-grandfather owes a fine of 30c for 100 years. If a penalty owed grows exponentially at 5% per year in continuous compound interest, how much would you have? What to pay if you return the book today? Rta. 44.52

(D

3 − 3DD

′2 − 2D

′3

)z = cos(x + 2y)