Solutions

In[14]:=

(*3.1*)DSolve[{y '[x] + 3y[x] 2, y[0] 1}, y[x], x]

Out[14]=

{{y[x] 1/3 ^(-3 x) (1 + 2 ^(3 x))}}

In[15]:=

(*3.2*)DSolve[{x '[t] + Sin[t] x[t] 0, x[0] 1}, x[t], t] Plot[x[t]/.%, {t, -Pi, Pi}]

Out[15]=

{{x[t] ^(-1 + Cos[t])}}

[Graphics:../HTMLFiles/ex05_solutions_34.gif]

Out[16]=

⁃Graphics⁃

In the next one, the symbols K$xxxx stand for variables.

In[17]:=

(*3.3*)DSolve[f '[x] + p[x] f[x] q[x], f[x], x]

Out[17]=

{{f[x] ^(∫_1^x -p[K$338] K$338) C[1] + ^(∫_1^x - ... 8;K$338) ∫_1^x^(-∫_1^K$357 -p[K$338] K$338) q[K$357] K$357}}

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