Step-by-step Solution

Solve the differential equation $\frac{dy}{dx}=e^{\left(2x+3y\right)}$

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=e^{2x+3y}$

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}=e^{2x}e^{3y}$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=e^(2x+3y). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side. Integrate both sides, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{e^{3y}}dy and replace the result in the differential equation.

Final Answer

$y=\frac{\ln\left(-3\left(\frac{1}{2}e^{2x}+C_0\right)\right)}{-3}$

Problem Analysis