Differential Equations and Linear Algebra fcf(x) dx = cff(x) dx when c is a constantff(x) + g(x) dx = f f(x) dx +g(x) dxfk dxfx" dx = 1+¹+C when n ‡ −1= In x + Cdx = e + CS=dxSex= kx + C when k is a constantfb² dx = √b² + C when b>0Inf sin x daf cos x dx ==f sec² x dx =csc² x dx=sin x + Ccos x + Ctan x + Cf secx tan x dxfcscx cotx dxcotx + C=secx + C= csc x + CS dx = arctanr +C1²+1S da = arcsin x + C-x:2f sinh x dx = cosh x + Csinh and cosh are hyperbolic sine and hyperbolic cosinef cosh x dx = sinh x + C sinh and cosh are hyperbolic sine and hyperbolic cosine Solve the following ODE. Be sure to state what type of ODE it is at the beginning. If you perform some trickery toconvert the ODE into a different type you should also write what type it has changed into. In short, include every littlestep (that includes every step in the antiderivatives too. Remember this list.) Your solution must be clear, complete, anddetailed.+ tan(x) y=sin(2x)

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Answered: Solve the following ODE. Be sure to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations and Linear Algebra

fcf(x) dx = cff(x) dx when c is a constant
ff(x) + g(x) dx = f f(x) dx +
g(x) dx
fk dx
fx" dx = 1+¹+C when n ‡ −1
= In x + C
dx = e + C
S=dx
Sex
= kx + C when k is a constant
fb² dx = √b² + C when b>0
In
f sin x da
f cos x dx =
=
f sec² x dx =
csc² x dx
=
sin x + C
cos x + C
tan x + C
f secx tan x dx
fcscx cotx dx
cotx + C
=
secx + C
= csc x + C
S dx = arctanr +C
1
²+1
S da = arcsin x + C
-x:2
f sinh x dx = cosh x + C
sinh and cosh are hyperbolic sine and hyperbolic cosine
f cosh x dx = sinh x + C sinh and cosh are hyperbolic sine and hyperbolic cosine

Solve the following ODE. Be sure to state what type of ODE it is at the beginning. If you perform some trickery to
convert the ODE into a different type you should also write what type it has changed into. In short, include every little
step (that includes every step in the antiderivatives too. Remember this list.) Your solution must be clear, complete, and
detailed.
+ tan(x) y
=
sin(2x)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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