# SECTION 7.1# Example 1

de := diff(x(t),t) + 3/500*x(t) = g(t);

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with(inttrans);

NiM3LyUpYWRkdGFibGVHJShmb3VyaWVyRyUrZm91cmllcmNvc0clK2ZvdXJpZXJzaW5HJSdoYW5rZWxHJShoaWxiZXJ0RyUraW52Zm91cmllckclK2ludmhpbGJlcnRHJStpbnZsYXBsYWNlRyUqaW52bWVsbGluRyUobGFwbGFjZUclJ21lbGxpbkclKnNhdmV0YWJsZUc=

lde := laplace(de,t,s);

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alias(X = laplace(x(t),t,s));alias(G = laplace(g(t),t,s));

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lde;

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subs(x(0)=30,%);

NiMvLCgqJiUic0ciIiIlIlhHRidGJyIjSSEiIiomIyIiJCIkKyZGJ0YoRidGJyUiR0c=

solve(%,X);

NiMsJCooIiQrJiIiIiwmIiNJRiYlIkdHRiZGJiwmKiZGJUYmJSJzR0YmRiYiIiRGJiEiIkYm

X := %;

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?piecewiseg1(t) := piecewise(t>0 and t<10, 2.4, t>10, 1.2);

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plot(g1(t),t=0..20);

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

laplace(g1(t),t,s);

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G1 := %;

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X := 500*(30+G1)/(500*s+3);

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invlaplace(X,s,t);

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xsol := %;

NiM+JSV4c29sRywoKiYkIiRxJCIiISIiIi0lJGV4cEc2IywkKiYkIisrKysrZyEjN0YqJSJ0R0YqISIiRipGNCQiJCslRilGKiooJCIkKyNGKUYqLSUqSGVhdmlzaWRlRzYjLCYkIiM1RilGNEYzRipGKiwmJEYqRilGKiomJEYqRilGKi1GLDYjLCYqJiQiKysrKytnRjJGKkYzRipGNCQiKysrKytnISM2RipGKkY0RipGNA==

convert(xsol,piecewise);

NiMtJSpQSUVDRVdJU0VHNiU3JCwmKiYkIiRxJCIiISIiIi0lJGV4cEc2IywkKiYkIisrKysrZyEjN0YsJSJ0R0YsISIiRixGNiQiJCslRitGLDJGNSQiIzVGKzckJEYsJSp1bmRlZmluZWRHL0Y1Rjo3JCwoKiYkRipGK0YsRi1GLEY2JCIkKyNGK0YsKiZGREYsLUYuNiMsJiomJCIrKysrK2dGNEYsRjVGLEY2JCIrKysrK2chIzZGLEYsRiwyRjpGNQ==

plot(%,t=0..250);

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