What is a solution to the differential equation $e^{y} \frac{d y}{d t} = 3 t^{2} + 1$ $e^ydy/dt=3t^2+1$ ?

Question

What is a solution to the differential equation $e^{y} \frac{d y}{d t} = 3 t^{2} + 1$ $e^ydy/dt=3t^2+1$ ?

1 Answer

Impact of this question

2270 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-01T15:43:13

$y = {log}_{e} (t^{3} + t + C)$ $y = log_e(t^3+t+C)$

Explanation:

$e^{y} \frac{d y}{d t} = 3 t^{2} + 1$ $e^ydy/dt=3t^2+1$ grouping variables
$e^{y} d y = (3 t^{2} + 1) d t \to e^{y} = t^{3} + t + C$ $e^y dy=(3t^2+1)dt->e^y = t^3+t+C$

Finally

$y = {log}_{e} (t^{3} + t + C)$ $y = log_e(t^3+t+C)$

Science

Math

Humanities

... and beyond

What is a solution to the differential equation $e^{y} \frac{d y}{d t} = 3 t^{2} + 1$ $e^ydy/dt=3t^2+1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is a solution to the differential equation e^ydy/dt=3t^2+1eydydt=3t2+1e^ydy/dt=3t^2+1?

1 Answer

Explanation:

Related questions

Impact of this question

What is a solution to the differential equation $e^{y} \frac{d y}{d t} = 3 t^{2} + 1$ $e^ydy/dt=3t^2+1$ ?