Q.1 Use Reduction of order method to find the second solution of dx 4x dy dx...
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Q.1 Use Reduction of order method to find the second solution of dx 4x dy dx #6y=0if y₁ = x² + x³ is the first solution. Q.2 (1) parameters. (ii) Q. 3 (1) (ii) Solve the differential equation Solve the Cauchy-Euler equation.x Solve the differential equation d'y dy -2 + y = dx² dx Find the general solution of 2 d²y dy +9x- dx² dx d^y 16 +24- dx-4 d³ y dy -16- 5 dxs dx d²y dx² : 0. et 1 + x² = -20y: by the Variation of 5 +9y = 0. d'y dx² dx dy Q. 4 (1) Solve the differential equation +9y=6x² +2-12e³ by undetermined dy coefficients (UC) method and verify particular integral by inverse operator method. (ii) Find a second solution of the equation x² -x- +2y=0 if y₁=xsin (In x) is the first dx² solution of the equation. dx Q. 5 A vertical beam of light passes through a transparent substance, the rate at which its intensity I decreases is proportional to I(t). In clear sea water the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. What is the intensity of the beam 15 feet below the surface? Here is the depth of the sea in feet. Model the differential equation of this problem using some physical law and hence determine the required. Q.1 Use Reduction of order method to find the second solution of dx 4x dy dx #6y=0if y₁ = x² + x³ is the first solution. Q.2 (1) parameters. (ii) Q. 3 (1) (ii) Solve the differential equation Solve the Cauchy-Euler equation.x Solve the differential equation d'y dy -2 + y = dx² dx Find the general solution of 2 d²y dy +9x- dx² dx d^y 16 +24- dx-4 d³ y dy -16- 5 dxs dx d²y dx² : 0. et 1 + x² = -20y: by the Variation of 5 +9y = 0. d'y dx² dx dy Q. 4 (1) Solve the differential equation +9y=6x² +2-12e³ by undetermined dy coefficients (UC) method and verify particular integral by inverse operator method. (ii) Find a second solution of the equation x² -x- +2y=0 if y₁=xsin (In x) is the first dx² solution of the equation. dx Q. 5 A vertical beam of light passes through a transparent substance, the rate at which its intensity I decreases is proportional to I(t). In clear sea water the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. What is the intensity of the beam 15 feet below the surface? Here is the depth of the sea in feet. Model the differential equation of this problem using some physical law and hence determine the required.
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Q1 To use the reduction of order method we assume that the second solution is of the form y uxy where ux is an unknown function to be determined We first find the first and second derivatives of y y x... View the full answer
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