Question

Solve the differential equation y'=3t^2+4. Solve the initial value problem y(0)=3.

Separation of variables!

My work:
dy/dt= 3t^2+4
dy= 3t^2+4 dt
Then you integrate both sides.
∫ dy= ∫ 3t^2+4dt
Question: is there a 1 in dy? ( ∫ 1dy)? If so:
y+C1=t^3+4t+C2
y=t^3+4t+C (where c is constant)

Then you find C
y(0)=3
3= 0+0 +C , So C=3

Ans: y=t^3+4t+3

Is this correct? Thank you!

Answer 1

I agree

Answer 2

[AI-generated answer — Explain Bot]

Yes, your solution is correct! You have correctly applied separation of variables to the differential equation and integrated both sides. Then, by taking into account the initial condition y(0) = 3, you found the constant C to be 3. Finally, you substituted C into the solution to obtain the final solution y = t^3 + 4t + 3. Well done!