Second and Third Order DEs-Differential Equations-Paper Solution, Exams of Differential Equations and Transforms

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PAKISTAN INSTITUTE OF ENGINEERING AND APPLIED SCIENCES BS (ME), 2" Semester Differential Equations SESSIONAL TEST-II Time Allowed: 1 hour 40 minutes : Total Marks: 25 Date: June 9, 2011 Attempt the following questions. 1. Find a general solution of the equation yp +y=tanx (4) by the method of variation of parameters. 2, Use the method of variation of parameters to find a general solution of the equation y" +9y = 2Sec3x (5) 3. Using the definition of Laplace transform, prove that Le je HE where ais realanda>-1 {4} 4. Solve the initial value problem by Laplace transform method 2 a +4x=Sin3t, x(0)=x'(0)=0 (4) 5. Solve the system by Laplace transform method L x"+x' ty’ +2x-y=0 y+x'+y'+4x—-2y=0 (5) xQ)=yO=1 x'O)=y0)=0 6. Find the convolution f= gt), where : fet and g()=e" (3) Page 1/1 docsity.com