# Differential Equation Questions Worksheet

## Differential Equation Questions Worksheet

International Association University Summer Sessions (IAUSS) Assignment 1 Differential Equation Summer Session 2020 Mr. HernΓ‘ndez Studentβs Name: 1) State the type and order of the given differential equation. Determinate whether or not the equation is linear, if nonlinear explain why? Identify the dependent and independent variables. a) π₯ b) π3 π¦ ππ¦ 4 ππ₯ ππ₯ β( ) +π¦ = 0 3 π4 π’ π2 π’ ππ₯ ππ¦ 2 +5 4 β 0.33π’ = 0 2) Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution: a) π¦ β²β² β 6π¦ β² + 13π¦ = 0; π¦ = π 3π₯ cos 2π₯ 3) Verify that the indicated expression is an implicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution: a) ππ ππ‘ = (π β 1)(1 β 2π); 2πβ1 ln ( πβ1 ) = π‘ 4) Verify that the function π(π₯ ) = π1 π π₯ + π2 π β2π₯ is a solution to the linear equation π2 π¦ ππ₯ 2 ππ¦ + ππ₯ β 2π¦ = 0, for any choice of the constants ππ and ππ . Determine ππ and ππ so that the initial condition π¦(0) = 2, π¦ β² (0) = 1 is satisfied. 5) Solve the initial value problem using βseparable variableβ ππ¦ ππ₯ π¦β1 = π₯+3 ; π¦(β1) = 0 6) Give an example of a Homogenous and a nonhomogeneous linear differential equation. 1 of 2 7) Heart Pacemaker consists of a switch, battery of constant voltage πΈ0 , a capacitor with constant capacitance πΆ, and the heart as a resistor with constant resistance R. When the switch is closed, the capacitor charges; when the switch is open, the capacitor discharges, sending an electrical stimulus to the heart. During the time the heart is being stimulated, the voltage πΈ across the heart satisfies the linear differential equation ππΈ 1 =β πΈ. ππ‘ ππΆ Solve the DE subject to πΈ (4) = πΈ0 . 8) In the following exercises determine whether the given D.E. is exact. If itβs exact, solve it. If not, find the multiple for exactness and then solve it. a) (2π¦ β 6π₯ )ππ₯ + (3π₯ + 4π₯ 2 π¦ β1 )ππ¦ = 0 ππ¦ b) π₯ ππ₯ = 2π₯π 2 β π¦ + 6π₯ 2 9) In 1790 the population of the United States was 3.93 million, and in 1890 it was 62.98 million. Using the Malthusian model [π(π‘) = π0 π ππ‘ ], estimate the U.S. population as a function of time. Use your result to predict the population in 1900. 2 of 2 …
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