Evaluate the laplace transform for this (a)L\{4x^2-3\cos(2x)+5e^x\} (b)L\{4+\frac{1}{2}\sin(x)-e^{4x}\}

ka1leE 2021-09-03 Answered

Evaluate the laplace transform for this
a)L{4x23cos(2x)+5ex}
b)L{4+12sin(x)e4x}

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Expert Answer

opsadnojD
Answered 2021-09-04 Author has 95 answers

Step 1 Introduction
Use following laplace formulas in solving following problems
1) L{1}=1s
2) L{xn}=n!sn+1
3) L{cosax}=ss2+a2
4) L{sinax}=as2+a2
5) L{eax}=1sa
Step 2 Step-by-Step Explanation
a)L{4x23cos(2x)+5ex}
by the linearity property
=4L{x2}3L{cos(2x)}+5L{ex}
=4(2!s3)3(ss2+22)+5(1s1)
=8s33ss2+4+5s1
b) L{4+12sin(x)e4x}
by the linearity property
=4L{1}+12L{sin(x)}L{e4x}
=4(1s)+12(1s2+1)1s4
=4s+12(s2+1)1s4
Result:
a) L{4x23cos(2x)+5ex}=8s33ss2+4+5s1
b) L{4+12sin(x)e4x}=4s+12(s2+1)1s4

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