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Solve the differential equation $y^{\prime}-2y=x^2+5$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\left(\frac{-x^2}{2e^{2x}}+\frac{-11}{4e^{2x}}+\frac{-x}{2e^{2x}}+C_0\right)e^{2x}$
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Step-by-step Solution

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Reescribir la ecuación diferencial utilizando la notación de Leibniz

$\frac{dy}{dx}-2y=x^2+5$

Learn how to solve definite integrals problems step by step online.

$\frac{dy}{dx}-2y=x^2+5$

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Learn how to solve definite integrals problems step by step online. Solve the differential equation y^'-2y=x^2+5. Reescribir la ecuación diferencial utilizando la notación de Leibniz. Podemos darnos cuenta de que la ecuación diferencial tiene la forma: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), así que podemos clasificarla en una ecuación diferencial lineal de primer orden, donde P(x)=-2 y Q(x)=x^2+5. Para poder resolver esta ecuación diferencial, el primer paso es encontrar el factor integrante \mu(x). Para encontrar \mu(x), primero necesitamos calcular \int P(x)dx. Asi que el factor integrante \mu(x) es.

Final answer to the problem

$y=\left(\frac{-x^2}{2e^{2x}}+\frac{-11}{4e^{2x}}+\frac{-x}{2e^{2x}}+C_0\right)e^{2x}$

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Linear Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

Plotting: $y=\left(\frac{-x^2}{2e^{2x}}+\frac{-11}{4e^{2x}}+\frac{-x}{2e^{2x}}+C_0\right)e^{2x}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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