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Solution set for Home Assignment # 2
H2.1:
Part Solution
(a) Algebraic, non-linear
(b) Differential, non-linear
© Differential, linear
H2.2:
Solution Equation (a) (b) © (d) (i) differential differential differential -
(ii) PDE ODE ODE -
(iii) 1 order w.r.t. x and t
2 order w.r.t. x
1 order w.r.t. t
(iv) linear linear Non-linear -
(v) homogenous If g≠0 then non- homogenous
If g=0 then homogenous
Non- homogenous
It is not algebraic
(vi) x, t x t Transcendental Equation
(vii) C u T Non-linear
(viii)
(ix)
(x)
Problem #
Problem Solution
1.1.1 y’=-sin(πx) cos(πx)/ π +c
1.1.4 y’= cosh(4x) y=sinh(4x)/4 +c
1.1.5 y’==1+y 2 First order, y=tan(x+c) 1.1.6 y’’+ π^2 y=0 Second order, y=acos(πx)+bsin(πx) 1.1.11 y’=1+4y 2 y=0.5tan(2x+c) y(0)=
Particular solution: y=0.5tan(2x+ nπ) n=0,±0, ±2,….
Plot: do it by yourself 1.1.13 y’+2xy= y=cexp(-x 2 ) y(1)=1/exp(1)
y= exp(-x 2 ) Plot: do it yourself
1.1.19 --read from your book--- 94m/s
1.1.21 --read from your book--- 1570years
1.2.11 y’=sin(πx/2) Exact solution y=(-2/π)cos(πx /2)+c
