Unformatted text preview: Muhammad Ulhaque due 2/24/08 at 11:55 PM. Assignment 4 MATH263, Winter 2008
. Try y p x 1.(1 pt) Find y as a function of x if 4y 128e 2x y 4 4y Correct Answers: y0 18 y 0 22 y 0 4 y 0 16 (P*x^2 + Q*x + R)*exp(-6*x) yx (P*x^3 + Q*x^2 + R*x)*exp(x) Correct Answers: P*x^3 + Q*x^2 + R*x 17 + 14*x + 3*e^(2*x) + -2*x*e^(2*x) + -2 * e^(-2*x) (P*x + Q)*exp(-6*x) + R*x 2.(1 pt) Find a particular solution to 5.(1 pt) The solution of the differential equation y 4y 3y 1xe5x y 9y 54 cos 3x 42 sin 3x y1 9 y 1 4 + a*e**(-4*x) + b*e**(5*x) y 4.(1 pt) This question is designed to test your ability to forCorrect Answers: mulate the correct try in the method of undetermined coeffi-0.666666666666667 * x**5 - 8.13333333333333 * x**-1 cients. For each of the following equations you must enter the 7.(1 pt) Find a particular solution to correct try for a particular solution. The undetermined coefficients must be the upper case letters P, Q, R, S, T etc. startdy d2y x2 2 5x 3y x2 cos x ing at P and using as many as you need in order. If you need dx dx three coefficients, then use P, Q and R. If you need four coin x 0. efficients, then use P, Q, R and S. Answers with unnecessary yp coefficients will not be accepted. Also please note that WebCorrect Answers: work will not accept complex numbers. Thus instead of entering ((x**-3)*(x^4*sin(x)+4*x^3*cos(x)-12*x^2*sin(x)+24*si Pe 3 2i x Qe 3 2i x you must enter the equivalent real-variable 8.(1 pt) Given that y x is a solution of form e3x P cos 2x Q sin 2x . Do not solve for the undetermined coefficients. Even if you replace one or more coefficients d2y dy x2 2x 3x2 tan 3x 2 3x tan 3x y 0 with their correct values, your answer will be marked incorrect. dx2 dx in x 0, find another solution yc of the same equation such that x yc x is a fundamental set of solutions. y 5y 6y x2 e 6x yc . Try y p x Correct Answers: v*(x*sin(3*x)) + u*x Try y p x Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR 1 1 y 3y 1 xe 6x Try y p x . " y 5y 6y x2 du by making the substitution y u 1 . dx The solution is y . Enter a function of x. Correct Answers: (5*(6-1)*x**5 - 6*(5-1)*x**6)/(x*((6-1)*x**5 - (5-1)* ! y y 9y 9y x2 5 ex . 9.(1 pt) Solve the first order initial value problem x2 dy dx 30 10xy x2y2 0 y1 1 ' $ & ) 0 Correct Answers: (27*x*x*x + -9*x*x + 2*x) * exp(5 *x) % % ( yp y y 20y 729x2e5x 6.(1 pt) Find y as a function of x if x2 y 3xy 5y x4 # yp subject to the initial conditions y 0 0 and y 0 7 is Correct Answers: yx (-0.0208333333333333 * x + 0.00607638888888889) * Correct Answers: exp(5*x) + a*e**(-1*x) + b*e**(-3*x) 3.(1 pt) Find a particular solution to 7*x*cos(3*x)+-9*x*sin(3*x) ...
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This note was uploaded on 06/09/2008 for the course MATH MATH 263 taught by Professor Humphire during the Spring '08 term at McGill.
- Spring '08