Question

Question 10: (1 point) We want to solve the differential equation dy/dx=[x(e^(7x+y^5)]/y4 a) This differential equation is separable and can be writen. ∫N(y)dy=∫M(x)dx , where M(x)= __________ and N(y)= __________ b) To compute the integral ∫N(y)dy, you need to use the substitution u= __________ With this substitution, we get ∫N(y)dy=∫n(u)du, where n(u)= __________ We find that ∫n(u)du=   __________  +K and hence ∫N(y)dy=   __________  +K, where we have added the constant of integration K for you; so you don't need to add one in your answer. c) To compute the integral ∫M(x)dx, you need to use integration by parts with f(x)= __________ and g′(x)= __________ With this choice, we get ∫M(x)dx=P(x)−∫Q(x)dx , where P(x)= __________ and Q(x)= __________ We then find that ∫M(x)dx=   __________  +D where we have added the constant of integration D for you; so you don't need to add one in your answer. d)Solve ∫N(y)dy=∫M(x)dx for y to find the general solution of the given differential equation. Then, give the particular solution satisfying the initial condition y(0)=0. y(x)=  __________

Answer 1